Finite Group Databasebeta

← C₁₃×Q₃₂ #88096

Subgroups — C₁₃×Q₃₂ #88096

Order 416.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×Q₁₆	C₂	1	2	yes	maximal
2	C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₃	—	2	2	no	—
4	C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₄×C₁₃	—	4	2	no	—
6	C₄×C₁₃	D₄	1	1	yes	characteristic
7	Q₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂×C₁₃	D₈	1	1	yes	characteristic
9	Q₁₆	C₂×C₁₃	1	2	yes	—
10	C₁₆	C₂×C₁₃	1	1	yes	characteristic
11	C₁₃	Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
12	Q₈	—	2	2	no	—
13	C₈	C₂²×C₁₃	1	1	yes	characteristic
14	C₄	—	4	2	no	—
15	C₄	D₄×C₁₃	1	1	yes	characteristic
16	C₂	C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₁₃	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₁₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. Q₃₂	C₁₃	direct (N × H)
11. C₁₃	Q₃₂	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×Q₁₆	2
C₁₃×C₁₆	2
Q₃₂	13